Public Key Exchange
draft-harkins-pkex-04
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draft-harkins-pkex-04
Internet Research Task Force D. Harkins
Internet-Draft HP Enterprise
Intended status: Informational July 28, 2017
Expires: January 29, 2018
Public Key Exchange
draft-harkins-pkex-04
Abstract
This memo describes a password-authenticated protocol to allow two
devices to exchange "raw" (uncertified) public keys and establish
trust that the keys belong to their respective identities.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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This Internet-Draft will expire on January 29, 2018.
Copyright Notice
Copyright (c) 2017 IETF Trust and the persons identified as the
document authors. All rights reserved.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Requirements Language . . . . . . . . . . . . . . . . . . 3
1.2. Notation . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Properties . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 5
4. Cryptographic Primitives . . . . . . . . . . . . . . . . . . 5
5. Protocol Definition . . . . . . . . . . . . . . . . . . . . . 6
5.1. Exchange Phase . . . . . . . . . . . . . . . . . . . . . 6
5.2. Commit/Reveal Phase . . . . . . . . . . . . . . . . . . . 7
6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 8
7. Security Considerations . . . . . . . . . . . . . . . . . . . 9
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 9
8.1. Normative References . . . . . . . . . . . . . . . . . . 9
8.2. Informative References . . . . . . . . . . . . . . . . . 10
Appendix A. Role-specific Elements . . . . . . . . . . . . . . . 10
A.1. ECC Role-specific Elements . . . . . . . . . . . . . . . 11
A.1.1. Role-specific Elements for NIST p256 . . . . . . . . 11
A.1.2. Role-specific Elements for NIST p384 . . . . . . . . 12
A.1.3. Role-specific Elements for NIST p521 . . . . . . . . 13
A.1.4. Role-specific Elements for brainpool p256r1 . . . . . 15
A.1.5. Role-specific Elements for brainpool p384r1 . . . . . 15
A.1.6. Role-specific Elements for brainpool p512r1 . . . . . 16
A.2. FFC Role-specific Elements . . . . . . . . . . . . . . . 17
A.2.1. Role-specific Elements for 2048-bit FFC group . . . . 18
A.2.2. Role-specific Elements for 3072-bit FFC group . . . . 19
A.2.3. Role-specific Elements for 4096-bit FFC group . . . . 21
A.2.4. Role-specific Elements for 8192-bit FFC group . . . . 24
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 30
1. Introduction
Many authenticated key exchange protocols allow for authentication
using uncertified, or "raw", public keys. Usually these
specifications-- e.g. [RFC7250] for TLS and [RFC7670] for IKEv2--
assume keys are exchanged in some out-of-band mechanism.
[RFC7250] further states that "the main security challenge [to using
'raw' public keys] is how to associate the public key with a specific
entity. Without a secure binding between identifier and key, the
protocol will be vulnerable to man-in-the- middle attacks."
The Public Key Exchange (PKEX) is designed to fill that gap: it
establishs a secure binding between exchanged public keys and
identifiers, it provides proof-of-possession of the exchanged public
keys to each peer, and it enables the establishment of trust in
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public keys that can subsequently be used to faccilitate
authentication in other authentication and key exchange protocols.
1.1. Requirements Language
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [RFC2119].
1.2. Notation
This memo describes a cryptographic exchange using sets of elements
called groups. Groups can be either traditional finite field or can
be based on elliptic curves. The public keys exchanged by PKEX are
elements in a group. Elements in groups are denoted in upper-case
and scalar values are denoted with lower-case. The generator of the
group is G.
When both the initator and responder use a similar, but unique, datum
it is denoted by appending an "i" for initiator or "r" for responder,
e.g. if each side needs an element C then the initiator's is Ci and
the responder's is Cr.
During the exchange, one side will generate data and the other side
will attempt to reconstruct it. The reconstructed data is "primed".
That is, if the initiator generates C then when responder tries to
reconstruct it, the responder will refer to it as C'. Data that is
directly sent and received is not primed.
The following notation is used in this memo:
C = A + B
The "group operation" on two elements, A and B, that produces a
third element, C. For finite field cryptography this is the
modular multiplication, for elliptic curve cryptography this is
point addition.
C = A - B
The "group operation" on element A and the inverse of element B
to produce a third element, C. Inversion is defined such that
the group operation on an element and its inverse results in the
identity element, the value one (1) for finite field cryptography
and the "point at infinity" for elliptic curve cryptography.
C = a * B
This denotes repeated application of the group operation to B--
i.e. B + B-- (a - 1) times.
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a = H(b)
A cryptographic hash function that takes data b of indeterminate
length and returns a fixed sized digest a.
a = F(B)
A mapping function that takes an element and returns a scalar.
For elliptic curve cryptography, F() returns the x-coordinate of
the point B. For finite field cryptography, F() is the identity
function.
a = KDF-b(c, d)
A key derivation function that derives an output key a of length
b from an input key c and context d.
a = HMAC(b, c)
A keyed MAC function that produces a digest a using key b and
text c.
a | b
Concatentation of data a with data b.
{a}b[c]
Authenticated-encryption of data (a), with a key (b), and
associated data (c) that is authenticated but not encrypted.
2. Properties
Subversion of PKEX involves an adversary being able to insert its own
public key into the exchange without the exchange failing, resulting
in one of the parties to the exchange believing the adversary's
public key actually belongs to the protocol peer.
PKEX has the following properties:
o An adversary is unable to subvert the exchange without knowing the
password.
o An adversary is unable to discover the password through passive
attack.
o The only information exposed by an active attack is whether a
single guess of the password is correct or not.
o Proof-of-possession of the private key is provided.
o At the end of the protocol, either trust is established in the
peer's public key and the public key is bound to the peer's
identity, or the exchange fails.
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3. Assumptions
Due to the nature of the exchange, only DSA ([DSS]) and ECDSA
([X9.62]) keys can be exchanged with PKEX.
PKEX requires fixed elements that are unique to the particular role
in the protocol, an initiator-specific element and a responder-
specific element. They need not be secret. It is assumed that both
parties know the role-specific elements for the particular group in
which their key pairs were derived. Techniques to generate role-
specific elements, and generated elements for popular groups, are
listed in Appendix A.1 and Appendix A.2.
The authenticated-encryption algorithm provides deterministic "key
wrapping". To achieve this the AE scheme used in PKEX is AES-SIV as
defined in [RFC5297].
The KDF provides for the generation of a cryptographically strong
secret key from an "imperfect" source of randomness. To achieve this
the KDF used in PKEX is the unsalted version of [RFC5869].
The keyed MAC function is HMAC per [RFC2104].
The following assumptions are made on PKEX:
o Only the peers involved in the exchange know the password.
o The peers' public keys are from the same group.
o The discrete logarithms of the public role-specific elements are
unknown, and determining them is computationally infeasible.
4. Cryptographic Primitives
HKDF and HMAC require an underlying hash function and AES-SIV
requires a key length. To provide for consistent security the hash
algorithm and key length depend on the group chosen to use with PKEX.
For ECC, the hash algorithm and key length depends on the size of the
prime defining the curve, p:
o SHA-256 and 256 bits: when len(p) <= 256
o SHA-384 and 384 bits: when 256 < len(p) <= 384
o SHA-512 and 512 bits: when 384 < len(p)
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For FFC, the hash algorithm depends on the prime, p, defining the
finite field:
o SHA-256 and 256 bits: when len(p) <= 2048
o SHA-384 and 384 bits: when 2048 < len(p) <= 3072
o SHA-512 and 512 bits: when 3072 < len(p)
5. Protocol Definition
PKEX is a balanced PAKE. The identical version of the password is
used by both parties.
PKEX consists of two phases: exchange and commit/reveal. It is
described using the popular protocol participants, Alice (an
initiator of PKEX), and Bob (a responder of PKEX).
We denote Alice's role-specific element a Pi and Bob's as Pr. The
password is pw. For simplicity, Alice's identity is "Alice" and
Bob's identity is "Bob". Alice's public key she wants to share with
Bob is A and her private key is a, while Bob's public key he wants to
share with Alice is B and his private key is b.
5.1. Exchange Phase
The Exchange phase is essentially the SPAKE2 key exchange. The peers
derive ephemeral public keys, encrypt, and exchange them. Each party
hashes a concatentation of his or her identity and the password and
operates on the role-specific element to obtain a secret encrypting
element. The group operation is then performed with the ephemeral
key and the secret encrypting element to produce an encrypted
ephmeral key.
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Alice: Bob:
------ ----
x, X = x*G y, Y = y*G
Qa = H(Alice|pw)*Pi Qr = H(Bob|pw)*Pr
M = X + Qa
M ------>
Qa = H(Alice|pw)*Pi
X' = M - Qa
N = Y + Qr
z = KDF-n(F(y*X'),
Alice | Bob |
F(M) | F(N) | pw)
<------ N
Qr = H(Bob|pw)*Pr
Y' = N - Qr
z = KDF-n(F(x*Y'),
Alice | Bob |
F(M) | F(N) | pw)
Both M and N MUST be verified to be valid elements in the selected
group. If either one is not valid the protocol fails.
At this point the peers have exchanged ephemeral elements that will
be unknown except by someone with knowledge of the password. Given
our assumptions that means only Alice and Bob can know the elements X
and Y, and the secret key, z.
The secret encrypting elements Qa and Qb SHALL be irretrievably
deleted at this point. The password MAY be irretrievably deleted at
this time.
5.2. Commit/Reveal Phase
In the Commit/Reveal phase the peers commit to the particular public
key they wish to exchange and reveal it to the peer. Proof-of-
possession of the private key is accomplished by "signing" the public
key, the identity to which the public key is bound, the receipient's
ephemeral public key, and the sender's ephemeral public key.
The messages exchanged in the Commit/Reveal phase are encrypted and
authenticated with AES-SIV using a key derived from the SPAKE2 key
exchange in Section 5.1. Successful construction and validation of
these messages authenticates the SPAKE2 exchange by proving
possession of the SPAKE2 shared secret and therefore knowledge of the
password. A single octet of the value zero (0) is used as associated
data when encrypting Alice's message to Bob and a single octet of the
value one (1) is used as associated data when constructing Bob's
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response. The associated data is not transferred as part of the
either message.
Alice: Bob:
------ ----
u = HMAC(F(a*Y'), Alice | F(A) |
F(Y') | F(X))
{A, u}z[0] ------>
if (SIV-decrypt returns fail) fail
if (A not valid element) fail
u' = HMAC(F(y*A), Alice | F(A) |
F(Y) | F(X'))
if (u' != u) fail
v = HMAC(F(b*X'), Bob | F(B) |
F(X') | F(Y))
<------ {B, v}z[1]
if (SIV-decrypt returns fail) fail
if (B not valid element) fail
v' = HMAC(F(x*B), Bob | F(B) |
F(X) | F(Y))
if (v'!= v) fail
where 0 and 1 are single octets of the value zero and one,
respectively, n is the key length from Section 4, and both the KDF
and HMAC use the hash algorithm from Section 4.
If the parties didn't fail they have each other's public key,
knowledge that the peer possesses the corresponding private key, and
trust that the public key belongs to the peer's identity that was
authenticated in the Exchange Phase.
All ephemeral state created during the PKEX exchange SHALL be
irretrievably deleted at this point.
6. IANA Considerations
This memo could create a registry of the fixed public elements for a
nice cross section of popular groups. Or not. Once published this
document will be a stable reference and a registry might not be
needed.
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7. Security Considerations
The encrypted shares exchanged in the Exchange phase MUST be
ephemeral. Reuse of these keys, even with a different password,
voids the security of the exchange.
If fixed elements other than those in Appendix A.1 and Appendix A.2
are used, their discrete logarithm MUST not be known. Knowledge of
of the discrete logarithm of either of the fixed elements voids the
security of the exchange.
The public keys exchanged in PKEX are never disclosed to an attacker,
either passive or active. While they are, as the name implies,
public, PKEX provides for secrecy of the exchanged keys for any
protocol that might need such a capability.
PKEX has forward secrecy in the sense that exposure of the password
used in a previous run of the protocol will not affect the security
of that run. This also means that once PKEX has finished, the
password can be exposed to a third party with out loss of security--
the public keys exchanged are still trusted and still bound to the
entities that performed the exchange originally.
The Exchange Phase of PKEX is SPAKE2. The SPAKE2 security proof
guarantees that if both sides bind the same password to each other's
identity they will derive the same secret. This means that the
public key sent in the Commit/Reveal phase is guaranteed to be sent
by the identified peer-- it is sent in a message that is integrity
protected and encrypted by a key, z, derived from the SPAKE2 shared
secret. This binds the peer's public key to its authenticated
identity. Proof-of-possession of the private key is provided by also
sending a digest keyed by the result of a function of the private key
and the peer's ephemeral share from the Exchange Phase. Since the
sender is not able to predict what random ephemeral share will be
received in the Exchange Phase, it is unable to generate a keyed
digest without knowing the private analog to the public key it is
sending.
There is no proof of security of PKEX at this time.
8. References
8.1. Normative References
[DSS] U.S. Department of Commerce/National Institute of
Standards and Technology, "Digital Signature Standard
(DSS)", Federal Information Processing Standards FIPS PUB
186-4, July 2013.
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[RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Hashing for Message Authentication", RFC 2104, DOI
10.17487/RFC2104, February 1997,
<http://www.rfc-editor.org/info/rfc2104>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC3526] Kivinen, T. and M. Kojo, "More Modular Exponential (MODP)
Diffie-Hellman groups for Internet Key Exchange (IKE)",
RFC 3526, DOI 10.17487/RFC3526, May 2003,
<http://www.rfc-editor.org/info/rfc3526>.
[RFC5297] Harkins, D., "Synthetic Initialization Vector (SIV)
Authenticated Encryption Using the Advanced Encryption
Standard (AES)", RFC 5297, DOI 10.17487/RFC5297, October
2008, <http://www.rfc-editor.org/info/rfc5297>.
[RFC5869] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
Key Derivation Function (HKDF)", RFC 5869, DOI 10.17487/
RFC5869, May 2010,
<http://www.rfc-editor.org/info/rfc5869>.
[X9.62] American National Standards Institute, "X9.62-2005",
Public Key Cryptography for the Financial Services
Industry (ECDSA), 2005.
8.2. Informative References
[RFC7250] Wouters, P., Ed., Tschofenig, H., Ed., Gilmore, J.,
Weiler, S., and T. Kivinen, "Using Raw Public Keys in
Transport Layer Security (TLS) and Datagram Transport
Layer Security (DTLS)", RFC 7250, DOI 10.17487/RFC7250,
June 2014, <http://www.rfc-editor.org/info/rfc7250>.
[RFC7670] Kivinen, T., Wouters, P., and H. Tschofenig, "Generic Raw
Public-Key Support for IKEv2", RFC 7670, DOI 10.17487/
RFC7670, January 2016,
<http://www.rfc-editor.org/info/rfc7670>.
Appendix A. Role-specific Elements
Role-specific elements for six popular elliptic curves and four
popular modp groups from [RFC3526] have been generated using the
following technique.
A loop is performed to generate role-specific elements by generating
a candidate, testing the candidate, and exiting the loop once the
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test succeeds. A single octet counter is incremented each time
through the loop (first time through the loop, the counter is one).
To find a candidate, a hash of an identifier (the concatenation of
the ASN.1 of the OID of the curve or the name of the FFC group), a
constant string, and the counter is produced. If the length of the
hash's digest is less than the desired bits, the digest is pre-pended
to the inputs and the result is fed back into the hash (this time it
is a hash of a concatentation of the old digest, asn.1, constant
string, counter) to produce the next length-of-digest bits. This is
repeated until the number of bits has been produced. Excess octets
are stripped off. The resulting string is interpreted as an integer
with the first octet of (the first) hash being the high-order octet
of the integer. For curves whose prime is not an integral number of
octets, the bitstring is right-shifted, pre-pending with zero bits,
in order to make a big-endian bitstring of the appropriate length.
If that resulting number is larger than the prime defining the group
the counter is incremented and the loop continues. Once an candidate
has been produced it is checked to see whether it is a valid element
in the group (for ECC it is treated as an x-coordinate and checked
whether it produces a valid point on the curve, for FFC it is checked
by seeing whether the exponentiation of the candidate to the power of
the prime minus one divided by the order, modulo the prime, is one).
If it is not, the counter is incremented and the whole loop is
performed again. This process is repeated until an element is found.
The hash algorithm used to generate candidates is determined by
Section 4.
The loop is performed twice for each elliptic curve and FFC group to
produce initiator- and responder-specific elements. The string
passed for the initiator-specific element is "PKEX Initiator", the
string passed for the responder-specific element is "PKEX Responder".
For FFC groups, the identifier is "group X" (including the space
character and excluding the quotation marks) where X is the id
assigned to the group, e.g. the 2048-bit group is named "group 14".
For ECC groups, the identifier is the DER-encoded ASN.1
representation of the OID of the curve.
A.1. ECC Role-specific Elements
A.1.1. Role-specific Elements for NIST p256
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unsigned char nist_p256_initiator_x_coord[32] = {
0x56, 0x26, 0x12, 0xcf, 0x36, 0x48, 0xfe, 0x0b,
0x07, 0x04, 0xbb, 0x12, 0x22, 0x50, 0xb2, 0x54,
0xb1, 0x94, 0x64, 0x7e, 0x54, 0xce, 0x08, 0x07,
0x2e, 0xec, 0xca, 0x74, 0x5b, 0x61, 0x2d, 0x25
};
unsigned char nist_p256_initiator_y_coord[32] = {
0x3e, 0x44, 0xc7, 0xc9, 0x8c, 0x1c, 0xa1, 0x0b,
0x20, 0x09, 0x93, 0xb2, 0xfd, 0xe5, 0x69, 0xdc,
0x75, 0xbc, 0xad, 0x33, 0xc1, 0xe7, 0xc6, 0x45,
0x4d, 0x10, 0x1e, 0x6a, 0x3d, 0x84, 0x3c, 0xa4
};
unsigned char nist_p256_responder_x_coord[32] = {
0x1e, 0xa4, 0x8a, 0xb1, 0xa4, 0xe8, 0x42, 0x39,
0xad, 0x73, 0x07, 0xf2, 0x34, 0xdf, 0x57, 0x4f,
0xc0, 0x9d, 0x54, 0xbe, 0x36, 0x1b, 0x31, 0x0f,
0x59, 0x91, 0x52, 0x33, 0xac, 0x19, 0x9d, 0x76
};
unsigned char nist_p256_responder_y_coord[32] = {
0x26, 0x04, 0x09, 0x45, 0x0a, 0x05, 0x20, 0xe7,
0xa7, 0x27, 0xc1, 0x36, 0x76, 0x85, 0xca, 0x3e,
0x42, 0x16, 0xf4, 0x89, 0x85, 0x34, 0x6e, 0xd5,
0x17, 0xde, 0xc0, 0xb8, 0xad, 0xfd, 0xb2, 0x98
};
A.1.2. Role-specific Elements for NIST p384
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unsigned char nist_p384_initiator_x_coord[48] = {
0x95, 0x3f, 0x42, 0x9e, 0x50, 0x7f, 0xf9, 0xaa,
0xac, 0x1a, 0xf2, 0x85, 0x2e, 0x64, 0x91, 0x68,
0x64, 0xc4, 0x3c, 0xb7, 0x5c, 0xf8, 0xc9, 0x53,
0x6e, 0x58, 0x4c, 0x7f, 0xc4, 0x64, 0x61, 0xac,
0x51, 0x8a, 0x6f, 0xfe, 0xab, 0x74, 0xe6, 0x12,
0x81, 0xac, 0x38, 0x5d, 0x41, 0xe6, 0xb9, 0xa3
};
unsigned char nist_p384_initiator_y_coord[48] = {
0x89, 0xd0, 0x97, 0x7b, 0x59, 0x4f, 0xa6, 0xd6,
0x7c, 0x5d, 0x93, 0x5b, 0x93, 0xc4, 0x07, 0xa9,
0x89, 0xee, 0xd5, 0xcd, 0x6f, 0x42, 0xf8, 0x38,
0xc8, 0xc6, 0x62, 0x24, 0x69, 0x0c, 0xd4, 0x48,
0xd8, 0x44, 0xd6, 0xc2, 0xe8, 0xcc, 0x62, 0x6b,
0x3c, 0x25, 0x53, 0xba, 0x4f, 0x71, 0xf8, 0xe7
};
unsigned char nist_p384_responder_x_coord[48] = {
0xad, 0xbe, 0xd7, 0x1d, 0x3a, 0x71, 0x64, 0x98,
0x5f, 0xb4, 0xd6, 0x4b, 0x50, 0xd0, 0x84, 0x97,
0x4b, 0x7e, 0x57, 0x70, 0xd2, 0xd9, 0xf4, 0x92,
0x2a, 0x3f, 0xce, 0x99, 0xc5, 0x77, 0x33, 0x44,
0x14, 0x56, 0x92, 0xcb, 0xae, 0x46, 0x64, 0xdf,
0xe0, 0xbb, 0xd7, 0xb1, 0x29, 0x20, 0x72, 0xdf
};
unsigned char nist_p384_responder_y_coord[48] = {
0x54, 0x58, 0x20, 0xad, 0x55, 0x1d, 0xca, 0xf3,
0x1c, 0x8a, 0xcd, 0x19, 0x40, 0xf9, 0x37, 0x83,
0xc7, 0xd6, 0xb3, 0x13, 0x7d, 0x53, 0x28, 0x5c,
0xf6, 0x2d, 0xf1, 0xdd, 0xa5, 0x8b, 0xad, 0x5d,
0x81, 0xab, 0xb1, 0x00, 0x39, 0xd6, 0xcc, 0x9c,
0xea, 0x1e, 0x84, 0x1d, 0xbf, 0xe3, 0x35, 0xf9
};
A.1.3. Role-specific Elements for NIST p521
Harkins Expires January 29, 2018 [Page 13]
Internet-Draft PKEX July 2017
unsigned char nist_p521_initiator_x_coord[66] = {
0x00, 0x16, 0x20, 0x45, 0x19, 0x50, 0x95, 0x23,
0x0d, 0x24, 0xbe, 0x00, 0x87, 0xdc, 0xfa, 0xf0,
0x58, 0x9a, 0x01, 0x60, 0x07, 0x7a, 0xca, 0x76,
0x01, 0xab, 0x2d, 0x5a, 0x46, 0xcd, 0x2c, 0xb5,
0x11, 0x9a, 0xff, 0xaa, 0x48, 0x04, 0x91, 0x38,
0xcf, 0x86, 0xfc, 0xa4, 0xa5, 0x0f, 0x47, 0x01,
0x80, 0x1b, 0x30, 0xa3, 0xae, 0xe8, 0x1c, 0x2e,
0xea, 0xcc, 0xf0, 0x03, 0x9f, 0x77, 0x4c, 0x8d,
0x97, 0x76
};
unsigned char nist_p521_initiator_y_coord[66] = {
0x01, 0x4c, 0x71, 0xfd, 0x1b, 0xd5, 0x9c, 0xa6,
0xed, 0x39, 0xef, 0x45, 0xc5, 0x06, 0xfd, 0x66,
0xc0, 0xeb, 0x0f, 0xbf, 0x21, 0xa3, 0x36, 0x74,
0xfd, 0xaa, 0x05, 0x6e, 0x4e, 0x33, 0x95, 0x42,
0x1a, 0x9d, 0x3f, 0x3a, 0x1c, 0x5e, 0xa8, 0x60,
0xf7, 0xe5, 0x59, 0x1d, 0x07, 0xaa, 0x6f, 0x40,
0x0a, 0x59, 0x3c, 0x27, 0xad, 0xe0, 0x48, 0xfd,
0xd1, 0x83, 0x37, 0x4c, 0xdf, 0xe1, 0x86, 0x72,
0xfc, 0x57
};
unsigned char nist_p521_responder_x_coord[66] = {
0x00, 0x79, 0xe4, 0x4d, 0x6b, 0x5e, 0x12, 0x0a,
0x18, 0x2c, 0xb3, 0x05, 0x77, 0x0f, 0xc3, 0x44,
0x1a, 0xcd, 0x78, 0x46, 0x14, 0xee, 0x46, 0x3f,
0xab, 0xc9, 0x59, 0x7c, 0x85, 0xa0, 0xc2, 0xfb,
0x02, 0x32, 0x99, 0xde, 0x5d, 0xe1, 0x0d, 0x48,
0x2d, 0x71, 0x7d, 0x8d, 0x3f, 0x61, 0x67, 0x9e,
0x2b, 0x8b, 0x12, 0xde, 0x10, 0x21, 0x55, 0x0a,
0x5b, 0x2d, 0xe8, 0x05, 0x09, 0xf6, 0x20, 0x97,
0x84, 0xb4
};
unsigned char nist_p521_responder_y_coord[66] = {
0x01, 0xb9, 0x9c, 0xc6, 0x41, 0x32, 0x5b, 0xd2,
0x35, 0xd8, 0x8b, 0x2b, 0xe4, 0x6e, 0xcc, 0xdf,
0x7c, 0x38, 0xc4, 0x5b, 0xf6, 0x74, 0x71, 0x5c,
0x77, 0x16, 0x8a, 0x80, 0xa9, 0x84, 0xc7, 0x7b,
0x9d, 0xfd, 0x83, 0x6f, 0xae, 0xf8, 0x24, 0x16,
0x2f, 0x21, 0x25, 0x65, 0xa2, 0x1a, 0x6b, 0x2d,
0x30, 0x62, 0xb3, 0xcc, 0x6e, 0x59, 0x3c, 0x7f,
0x58, 0x91, 0x81, 0x72, 0x07, 0x8c, 0x91, 0xac,
0x31, 0x1e
};
Harkins Expires January 29, 2018 [Page 14]
Internet-Draft PKEX July 2017
A.1.4. Role-specific Elements for brainpool p256r1
unsigned char brainpool_p256r1_initiator_x_coord[32] = {
0x46, 0x98, 0x18, 0x6c, 0x27, 0xcd, 0x4b, 0x10,
0x7d, 0x55, 0xa3, 0xdd, 0x89, 0x1f, 0x9f, 0xca,
0xc7, 0x42, 0x5b, 0x8a, 0x23, 0xed, 0xf8, 0x75,
0xac, 0xc7, 0xe9, 0x8d, 0xc2, 0x6f, 0xec, 0xd8
};
unsigned char brainpool_p256r1_initiator_y_coord[32] = {
0x16, 0x30, 0x68, 0x32, 0x3b, 0xb0, 0x21, 0xee,
0xeb, 0xf7, 0xb6, 0x7c, 0xae, 0x52, 0x26, 0x42,
0x59, 0x28, 0x58, 0xb6, 0x14, 0x90, 0xed, 0x69,
0xd0, 0x67, 0xea, 0x25, 0x60, 0x0f, 0xa9, 0x6c
};
unsigned char brainpool_p256r1_responder_x_coord[32] = {
0x90, 0x18, 0x84, 0xc9, 0xdc, 0xcc, 0xb5, 0x2f,
0x4a, 0x3f, 0x4f, 0x18, 0x0a, 0x22, 0x56, 0x6a,
0xa9, 0xef, 0xd4, 0xe6, 0xc3, 0x53, 0xc2, 0x1a,
0x23, 0x54, 0xdd, 0x08, 0x7e, 0x10, 0xd8, 0xe3
};
unsigned char brainpool_p256r1_responder_y_coord[32] = {
0x2a, 0xfa, 0x98, 0x9b, 0xe3, 0xda, 0x30, 0xfd,
0x32, 0x28, 0xcb, 0x66, 0xfb, 0x40, 0x7f, 0xf2,
0xb2, 0x25, 0x80, 0x82, 0x44, 0x85, 0x13, 0x7e,
0x4b, 0xb5, 0x06, 0xc0, 0x03, 0x69, 0x23, 0x64
};
A.1.5. Role-specific Elements for brainpool p384r1
Harkins Expires January 29, 2018 [Page 15]
Internet-Draft PKEX July 2017
unsigned char brainpool_p384r1_initiator_x_coord[48] = {
0x0a, 0x2c, 0xeb, 0x49, 0x5e, 0xb7, 0x23, 0xbd,
0x20, 0x5b, 0xe0, 0x49, 0xdf, 0xcf, 0xcf, 0x19,
0x37, 0x36, 0xe1, 0x2f, 0x59, 0xdb, 0x07, 0x06,
0xb5, 0xeb, 0x2d, 0xae, 0xc2, 0xb2, 0x38, 0x62,
0xa6, 0x73, 0x09, 0xa0, 0x6c, 0x0a, 0xa2, 0x30,
0x99, 0xeb, 0xf7, 0x1e, 0x47, 0xb9, 0x5e, 0xbe
};
unsigned char brainpool_p384r1_initiator_y_coord[48] = {
0x54, 0x76, 0x61, 0x65, 0x75, 0x5a, 0x2f, 0x99,
0x39, 0x73, 0xca, 0x6c, 0xf9, 0xf7, 0x12, 0x86,
0x54, 0xd5, 0xd4, 0xad, 0x45, 0x7b, 0xbf, 0x32,
0xee, 0x62, 0x8b, 0x9f, 0x52, 0xe8, 0xa0, 0xc9,
0xb7, 0x9d, 0xd1, 0x09, 0xb4, 0x79, 0x1c, 0x3e,
0x1a, 0xbf, 0x21, 0x45, 0x66, 0x6b, 0x02, 0x52
};
unsigned char brainpool_p384r1_responder_x_coord[48] = {
0x03, 0xa2, 0x57, 0xef, 0xe8, 0x51, 0x21, 0xa0,
0xc8, 0x9e, 0x21, 0x02, 0xb5, 0x9a, 0x36, 0x25,
0x74, 0x22, 0xd1, 0xf2, 0x1b, 0xa8, 0x9a, 0x9b,
0x97, 0xbc, 0x5a, 0xeb, 0x26, 0x15, 0x09, 0x71,
0x77, 0x59, 0xec, 0x8b, 0xb7, 0xe1, 0xe8, 0xce,
0x65, 0xb8, 0xaf, 0xf8, 0x80, 0xae, 0x74, 0x6c
};
unsigned char brainpool_p384r1_responder_y_coord[48] = {
0x2f, 0xd9, 0x6a, 0xc7, 0x3e, 0xec, 0x76, 0x65,
0x2d, 0x38, 0x7f, 0xec, 0x63, 0x26, 0x3f, 0x04,
0xd8, 0x4e, 0xff, 0xe1, 0x0a, 0x51, 0x74, 0x70,
0xe5, 0x46, 0x63, 0x7f, 0x5c, 0xc0, 0xd1, 0x7c,
0xfb, 0x2f, 0xea, 0xe2, 0xd8, 0x0f, 0x84, 0xcb,
0xe9, 0x39, 0x5c, 0x64, 0xfe, 0xcb, 0x2f, 0xf1
};
A.1.6. Role-specific Elements for brainpool p512r1
Harkins Expires January 29, 2018 [Page 16]
Internet-Draft PKEX July 2017
unsigned char brainpool_p512r1_initiator_x_coord[64] = {
0x4c, 0xe9, 0xb6, 0x1c, 0xe2, 0x00, 0x3c, 0x9c,
0xa9, 0xc8, 0x56, 0x52, 0xaf, 0x87, 0x3e, 0x51,
0x9c, 0xbb, 0x15, 0x31, 0x1e, 0xc1, 0x05, 0xfc,
0x7c, 0x77, 0xd7, 0x37, 0x61, 0x27, 0xd0, 0x95,
0x98, 0xee, 0x5d, 0xa4, 0x3d, 0x09, 0xdb, 0x3d,
0xfa, 0x89, 0x9e, 0x7f, 0xa6, 0xa6, 0x9c, 0xff,
0x83, 0x5c, 0x21, 0x6c, 0x3e, 0xf2, 0xfe, 0xdc,
0x63, 0xe4, 0xd1, 0x0e, 0x75, 0x45, 0x69, 0x0f
};
unsigned char brainpool_p512r1_initiator_y_coord[64] = {
0x5a, 0x28, 0x01, 0xbe, 0x96, 0x82, 0x4e, 0xf6,
0xfa, 0xed, 0x7d, 0xfd, 0x48, 0x8b, 0x48, 0x4e,
0xd1, 0x97, 0x87, 0xc4, 0x05, 0x5d, 0x15, 0x2a,
0xf4, 0x91, 0x4b, 0x75, 0x90, 0xd9, 0x34, 0x2c,
0x3c, 0x12, 0xf2, 0xf5, 0x25, 0x94, 0x24, 0x34,
0xa7, 0x6d, 0x66, 0xbc, 0x27, 0xa4, 0xa0, 0x8d,
0xd5, 0xe1, 0x54, 0xa3, 0x55, 0x26, 0xd4, 0x14,
0x17, 0x0f, 0xc1, 0xc7, 0x3d, 0x68, 0x7f, 0x5a
};
unsigned char brainpool_p512r1_responder_x_coord[64] = {
0x2a, 0x60, 0x32, 0x27, 0xa1, 0xe6, 0x94, 0x72,
0x1c, 0x48, 0xbe, 0xc5, 0x77, 0x14, 0x30, 0x76,
0xe4, 0xbf, 0xf7, 0x7b, 0xc5, 0xfd, 0xdf, 0x19,
0x1e, 0x0f, 0xdf, 0x1c, 0x40, 0xfa, 0x34, 0x9e,
0x1f, 0x42, 0x24, 0xa3, 0x2c, 0xd5, 0xc7, 0xc9,
0x7b, 0x47, 0x78, 0x96, 0xf1, 0x37, 0x0e, 0x88,
0xcb, 0xa6, 0x52, 0x29, 0xd7, 0xa8, 0x38, 0x29,
0x8e, 0x6e, 0x23, 0x47, 0xd4, 0x4b, 0x70, 0x3e
};
unsigned char brainpool_p512r1_responder_y_coord[64] = {
0x2a, 0xbe, 0x59, 0xe6, 0xc4, 0xb3, 0xd8, 0x09,
0x66, 0x89, 0x0a, 0x2d, 0x19, 0xf0, 0x9c, 0x9f,
0xb4, 0xab, 0x8f, 0x50, 0x68, 0x3c, 0x74, 0x64,
0x4e, 0x19, 0x55, 0x81, 0x9b, 0x48, 0x5c, 0xf4,
0x12, 0x8d, 0xb9, 0xd8, 0x02, 0x5b, 0xe1, 0x26,
0x7e, 0x19, 0x5c, 0xfd, 0x70, 0xf7, 0x4b, 0xdc,
0xb5, 0x5d, 0xc1, 0x7a, 0xe9, 0xd1, 0x05, 0x2e,
0xd1, 0xfd, 0x2f, 0xce, 0x63, 0x77, 0x48, 0x2c
};
A.2. FFC Role-specific Elements
Harkins Expires January 29, 2018 [Page 17]
Internet-Draft PKEX July 2017
A.2.1. Role-specific Elements for 2048-bit FFC group
unsigned char group14_initiator[256] = {
0x97, 0x15, 0x52, 0x05, 0x89, 0xdf, 0xeb, 0x3d,
0xd6, 0x50, 0xe1, 0x96, 0xd4, 0x30, 0x81, 0x04,
0x3a, 0x4d, 0x6c, 0xae, 0xe5, 0x81, 0xb6, 0x1d,
0x53, 0xca, 0x65, 0xfa, 0x19, 0x59, 0xfd, 0xe4,
0xa4, 0xf0, 0x7b, 0xc5, 0xc7, 0xc4, 0xa9, 0xd6,
0xdf, 0x79, 0x54, 0x04, 0x5d, 0x64, 0xdc, 0x3c,
0xec, 0x0a, 0xa0, 0xd3, 0x2f, 0xef, 0xf3, 0xf5,
0x2c, 0x51, 0xe6, 0x6d, 0x1c, 0xdc, 0xac, 0x09,
0x3c, 0x00, 0x62, 0x41, 0xe7, 0x0b, 0x0d, 0xba,
0x1b, 0xf2, 0xb9, 0x22, 0xe9, 0x11, 0xea, 0xc7,
0xb1, 0xb2, 0x15, 0xc5, 0x19, 0x46, 0x2e, 0x15,
0x88, 0x41, 0xe0, 0x24, 0x16, 0x13, 0xc1, 0x0e,
0x27, 0xd3, 0x5f, 0x71, 0x12, 0xc6, 0x6f, 0x75,
0x1e, 0xe8, 0xa4, 0xaa, 0x57, 0xa3, 0x22, 0x32,
0xdc, 0xd4, 0xe3, 0xb5, 0xa3, 0xd0, 0x87, 0xb1,
0x3d, 0x1c, 0x2a, 0xcf, 0xe5, 0x87, 0x1f, 0xea,
0x98, 0xdd, 0xd6, 0x8f, 0xce, 0x0b, 0xdd, 0xba,
0xae, 0x85, 0x81, 0xd6, 0x89, 0x27, 0x71, 0xc9,
0x9f, 0xf9, 0xea, 0x5a, 0x89, 0xa6, 0xaa, 0x0a,
0xc2, 0x76, 0xd6, 0x6d, 0x89, 0xd3, 0xd2, 0x4c,
0xc0, 0xad, 0xb0, 0xf6, 0x4d, 0x2b, 0x7c, 0xbf,
0xd2, 0x4e, 0xe3, 0x2b, 0x4f, 0xd7, 0xc5, 0x3a,
0x4b, 0x1c, 0xc0, 0x17, 0xbe, 0x1e, 0x7b, 0x81,
0x1c, 0x77, 0xd4, 0xc2, 0xf6, 0xca, 0xb8, 0x51,
0xa8, 0x94, 0xe9, 0xe5, 0xe9, 0xa5, 0x46, 0x60,
0xb5, 0x36, 0x10, 0xcf, 0xc8, 0x2a, 0xe7, 0x7f,
0x94, 0x49, 0x96, 0xeb, 0xff, 0x7b, 0x62, 0xa9,
0x95, 0x35, 0x5c, 0xad, 0xcd, 0x52, 0x06, 0xa1,
0x9c, 0xa1, 0xb7, 0xe0, 0xcd, 0xd3, 0x13, 0x43,
0xee, 0xe7, 0xf1, 0xb1, 0x4d, 0x76, 0x51, 0x53,
0x24, 0x4f, 0xb4, 0xbd, 0x8b, 0x0c, 0x73, 0xd1,
0x6f, 0xf5, 0x27, 0x3f, 0xb9, 0x60, 0xa6, 0x17
}
unsigned char group14_responder[256] = {
0x3c, 0x86, 0x96, 0x8a, 0xb0, 0x4b, 0x14, 0xdd,
0x27, 0xf0, 0x6f, 0x51, 0xa2, 0xb2, 0xbd, 0x7d,
0x27, 0x34, 0xf2, 0x21, 0x3c, 0x6a, 0x63, 0xcf,
0x15, 0xd8, 0xeb, 0x21, 0xc2, 0x2d, 0xe5, 0x75,
0xbb, 0x7e, 0x09, 0x2e, 0xba, 0xa2, 0xd7, 0x04,
0x7c, 0x81, 0x82, 0x07, 0x09, 0x15, 0x28, 0x35,
0xf7, 0x0a, 0xd6, 0xa9, 0xaf, 0x0d, 0xb1, 0x97,
0x71, 0x76, 0x74, 0x66, 0xa3, 0x54, 0x9e, 0xd9,
0xa9, 0x13, 0xa8, 0xcf, 0xec, 0xce, 0x60, 0xd8,
0xea, 0x18, 0x67, 0xb7, 0x15, 0x17, 0xf7, 0xe6,
Harkins Expires January 29, 2018 [Page 18]
Internet-Draft PKEX July 2017
0x23, 0xc8, 0x30, 0x02, 0xb9, 0x9e, 0x0e, 0xe6,
0x64, 0x3e, 0x1a, 0x61, 0xb9, 0xbf, 0xd8, 0x7a,
0x0e, 0xbe, 0x1e, 0x58, 0xdc, 0xba, 0x9e, 0x31,
0xab, 0xcc, 0x6b, 0x03, 0xcc, 0x08, 0xf8, 0xa2,
0xcb, 0x9d, 0xd5, 0x1a, 0xb8, 0x6a, 0x1f, 0x4b,
0xab, 0xe8, 0x2a, 0x0c, 0x44, 0xde, 0x2a, 0xfd,
0x0f, 0x6d, 0x2f, 0xe4, 0xc4, 0x41, 0x61, 0xed,
0x4a, 0x85, 0x2a, 0x06, 0x9d, 0x3a, 0x27, 0xf0,
0x30, 0x6e, 0xf8, 0xb1, 0xc8, 0xde, 0x1f, 0xe0,
0xfb, 0xb6, 0xd0, 0x51, 0xee, 0x7d, 0x3a, 0x05,
0x0c, 0xbb, 0xa0, 0x41, 0xc5, 0x5d, 0x25, 0xb4,
0x48, 0xd6, 0x4f, 0x08, 0x85, 0x96, 0xa3, 0xa6,
0xf5, 0x1b, 0xa1, 0xb3, 0x13, 0x50, 0x06, 0xb2,
0xef, 0xf8, 0x2f, 0xe8, 0x7b, 0xe0, 0x5a, 0xe1,
0x42, 0x16, 0xfc, 0xdf, 0xad, 0x53, 0x95, 0x43,
0xb0, 0x73, 0x33, 0xa9, 0x08, 0x29, 0xcd, 0x6c,
0x14, 0x98, 0x5e, 0x98, 0xe6, 0xca, 0x92, 0x55,
0xd9, 0x3e, 0xc3, 0x51, 0x83, 0xda, 0x1e, 0x6d,
0x16, 0x88, 0x3f, 0xd1, 0xa5, 0xd1, 0xc5, 0x43,
0xcf, 0x8a, 0xd7, 0x29, 0xaa, 0xa6, 0x4f, 0x6b,
0x4f, 0xee, 0x36, 0x65, 0xd6, 0x71, 0xef, 0x71,
0xc5, 0x5b, 0x7c, 0x6d, 0x90, 0x9d, 0xf5, 0x74
}
A.2.2. Role-specific Elements for 3072-bit FFC group
unsigned char group15_initiator[384] = {
0x12, 0xce, 0x47, 0xcf, 0xa9, 0xc4, 0xfc, 0x5e,
0x99, 0xf6, 0xd2, 0x43, 0x5c, 0x60, 0x39, 0xb0,
0x06, 0xe9, 0x4a, 0xec, 0x21, 0x60, 0x9f, 0x5a,
0x25, 0xb1, 0x22, 0xf2, 0x53, 0x2b, 0x44, 0xe3,
0x6c, 0xfb, 0x9c, 0x46, 0x3c, 0x8f, 0x88, 0xaa,
0x60, 0xfd, 0x3a, 0x51, 0xf1, 0x19, 0x8d, 0x88,
0xee, 0xa4, 0xc2, 0x21, 0x3c, 0xbb, 0xc5, 0x53,
0x12, 0x16, 0xfb, 0xd3, 0xa9, 0x4d, 0x85, 0x5d,
0x17, 0x9d, 0x92, 0x15, 0x30, 0xc7, 0x97, 0x0c,
0x68, 0x62, 0x91, 0xff, 0xce, 0x81, 0x97, 0x25,
0x54, 0x94, 0x0e, 0x3a, 0x14, 0x36, 0x4e, 0xc2,
0xda, 0xc2, 0xaa, 0xa3, 0x58, 0x49, 0xca, 0xa4,
0xa4, 0x0b, 0x2a, 0x26, 0x35, 0x0d, 0x72, 0x4f,
0x10, 0x3c, 0x5f, 0x4d, 0xbc, 0x7c, 0x09, 0xcb,
0xef, 0x99, 0xdd, 0x73, 0x1c, 0x23, 0x69, 0xa7,
0xc9, 0xc4, 0x1a, 0x4c, 0x7c, 0xf2, 0xca, 0x48,
0x15, 0xf4, 0xd6, 0x30, 0x25, 0x44, 0x9f, 0xcd,
0xc0, 0x23, 0x72, 0x4a, 0x4f, 0x83, 0x3c, 0xba,
0x88, 0x1c, 0x5a, 0xcc, 0x3f, 0xf6, 0x5e, 0x68,
0x5a, 0x38, 0x10, 0xa1, 0xd2, 0x99, 0x5f, 0x4d,
0x48, 0xec, 0xb1, 0x2f, 0x9a, 0x08, 0xcf, 0x59,
Harkins Expires January 29, 2018 [Page 19]
Internet-Draft PKEX July 2017
0x0f, 0xeb, 0x35, 0x0b, 0xf5, 0xab, 0x6e, 0xc9,
0x69, 0x44, 0xbd, 0x9a, 0x62, 0x3b, 0x53, 0x4e,
0x59, 0xc9, 0x38, 0x1d, 0x9e, 0x61, 0x5b, 0xdb,
0x72, 0x4e, 0xb9, 0x35, 0xb5, 0xc3, 0x9f, 0x47,
0x4f, 0x70, 0xfa, 0xff, 0x95, 0x45, 0xf9, 0x4a,
0xf4, 0xc3, 0xcc, 0x8e, 0xf4, 0x89, 0x0b, 0x73,
0x08, 0x97, 0x0d, 0x22, 0xe2, 0x97, 0xc8, 0xf8,
0x45, 0x83, 0x8f, 0xea, 0x68, 0x4b, 0xe0, 0xed,
0x71, 0xdb, 0x73, 0x62, 0x57, 0xab, 0x03, 0x69,
0x93, 0x66, 0x0e, 0xc1, 0x29, 0x2d, 0x01, 0x7c,
0x7d, 0x50, 0x14, 0x03, 0x9f, 0xdb, 0x5c, 0x4c,
0xf4, 0xdf, 0xa4, 0x9c, 0xda, 0x80, 0xd9, 0xbe,
0x0d, 0xdc, 0xb8, 0x0b, 0xc2, 0x19, 0x28, 0xaf,
0xf0, 0x98, 0x1a, 0xec, 0x26, 0xf0, 0x15, 0x1b,
0xa1, 0xa1, 0x11, 0x8f, 0x9f, 0x5a, 0x1e, 0x8a,
0x8e, 0x57, 0x84, 0x60, 0xc5, 0xda, 0xa2, 0x74,
0x3d, 0xe8, 0xc0, 0x08, 0x0f, 0x7e, 0xdd, 0x11,
0xd6, 0xbf, 0x5b, 0x2e, 0xde, 0x81, 0x1a, 0xfd,
0x33, 0x9c, 0x07, 0xcc, 0x1d, 0x0f, 0x63, 0xc8,
0x3e, 0x1d, 0xbb, 0x16, 0x5e, 0x70, 0x4c, 0x82,
0x8e, 0x72, 0xb6, 0x35, 0x69, 0xc6, 0xe4, 0xa7,
0xae, 0x6e, 0xa2, 0x23, 0xe8, 0x86, 0x99, 0x3a,
0x0b, 0x64, 0xec, 0xe2, 0xdb, 0xb2, 0xaa, 0xc4,
0x59, 0xe1, 0x23, 0x3d, 0xa5, 0x46, 0x92, 0x8f,
0x04, 0x34, 0x5f, 0x7a, 0x13, 0x55, 0x75, 0xd5,
0x6d, 0x0f, 0x5a, 0xc2, 0x0d, 0x16, 0xf9, 0xc0,
0xf3, 0xac, 0x0a, 0xa8, 0x62, 0x20, 0x09, 0x4e
}
unsigned char group15_responder[384] = {
0x9f, 0x17, 0xe0, 0xf9, 0x3d, 0x23, 0x36, 0x6e,
0x7d, 0xa6, 0x34, 0x75, 0xb7, 0xb4, 0x22, 0xb1,
0x87, 0x7a, 0x00, 0x4e, 0x02, 0x14, 0x4e, 0xe6,
0x96, 0xd4, 0x2c, 0x61, 0x00, 0x97, 0x7d, 0x99,
0xad, 0x18, 0x1c, 0xc4, 0x1b, 0xed, 0x6f, 0xd3,
0x9f, 0x85, 0xef, 0xfd, 0x1e, 0xcd, 0x13, 0xa0,
0x61, 0x2f, 0xf8, 0xa7, 0x11, 0xab, 0x83, 0xfc,
0xae, 0xad, 0xb6, 0xed, 0x6b, 0x7f, 0x34, 0x81,
0x30, 0xa2, 0x1c, 0x38, 0xb3, 0x31, 0x7b, 0x74,
0xc1, 0x0f, 0xf4, 0x29, 0x4b, 0xdd, 0x2b, 0x09,
0x32, 0xb7, 0x8f, 0x84, 0xab, 0x89, 0x9d, 0x64,
0xea, 0xec, 0x00, 0xa9, 0x0c, 0x82, 0x1c, 0x35,
0x75, 0x3b, 0x7f, 0x35, 0x28, 0xb8, 0xcc, 0xb1,
0x62, 0xc2, 0xd0, 0x74, 0x83, 0xb6, 0xf7, 0x76,
0x10, 0x2a, 0x7e, 0xce, 0xd0, 0x0a, 0x68, 0x46,
0xac, 0x78, 0x26, 0x90, 0xc7, 0x0e, 0xaa, 0x21,
0x59, 0xb1, 0x8d, 0x8e, 0xc8, 0xfb, 0x5c, 0x60,
0xec, 0x53, 0x9c, 0x40, 0xd9, 0x42, 0xab, 0xa3,
Harkins Expires January 29, 2018 [Page 20]
Internet-Draft PKEX July 2017
0xd8, 0x45, 0x81, 0x04, 0x6c, 0x13, 0x79, 0x66,
0x51, 0x1f, 0xa4, 0x81, 0x38, 0x0d, 0x48, 0x06,
0xef, 0x25, 0x89, 0x26, 0x5d, 0x09, 0x0e, 0xbe,
0xba, 0xe2, 0xca, 0x2c, 0xa6, 0x3e, 0x36, 0xd7,
0xef, 0x46, 0xe3, 0x8a, 0x1d, 0x85, 0x59, 0xc4,
0x89, 0x5e, 0x36, 0xea, 0xb2, 0x44, 0x79, 0xc8,
0x91, 0x80, 0x2c, 0x89, 0xfc, 0x55, 0x81, 0x62,
0x40, 0x82, 0x1a, 0x66, 0xf1, 0x1c, 0x10, 0xf0,
0x34, 0xdd, 0x52, 0x9f, 0xff, 0x63, 0x62, 0xe2,
0xec, 0x68, 0x75, 0xa0, 0x2e, 0x72, 0x44, 0xf3,
0x66, 0x33, 0x2a, 0x65, 0x61, 0x79, 0x91, 0x13,
0x4f, 0x73, 0x8f, 0x38, 0xef, 0xa6, 0x65, 0x88,
0xf9, 0x03, 0x35, 0x57, 0xed, 0xb9, 0x05, 0x7f,
0xe8, 0xfb, 0x90, 0xac, 0x19, 0x2e, 0xff, 0x9c,
0xaf, 0x76, 0x5f, 0x40, 0x74, 0x49, 0x11, 0xee,
0x18, 0xb5, 0x6e, 0xa4, 0x91, 0xbc, 0x42, 0x1c,
0x0e, 0x2e, 0x0d, 0x6f, 0xc3, 0x6a, 0x7b, 0x8b,
0xf4, 0x1a, 0x30, 0x52, 0x54, 0x99, 0xae, 0x8a,
0x8c, 0x33, 0x5e, 0x5c, 0xa8, 0xc2, 0x49, 0xf3,
0xbd, 0x0e, 0x85, 0x22, 0x9b, 0x5d, 0x92, 0xbc,
0x42, 0x8b, 0x60, 0x38, 0xd7, 0x14, 0x24, 0xaa,
0x36, 0xc7, 0x8f, 0xd7, 0xc2, 0x14, 0x20, 0x72,
0x0a, 0xba, 0x28, 0x95, 0x65, 0x53, 0x30, 0x0f,
0xc8, 0x17, 0xc2, 0x02, 0x58, 0x08, 0x7b, 0x93,
0x36, 0xcc, 0x80, 0x19, 0x9c, 0x1f, 0xad, 0x1f,
0x8e, 0x8e, 0x2e, 0x3a, 0xbf, 0x0f, 0xab, 0x76,
0x7a, 0xac, 0xce, 0x1a, 0x57, 0xe6, 0x7c, 0x64,
0x93, 0x5f, 0x92, 0x5d, 0xbe, 0xe2, 0x11, 0xf6,
0x58, 0x90, 0xd8, 0x87, 0xe4, 0x17, 0x8b, 0x61,
0xf6, 0x11, 0xe2, 0x0a, 0x99, 0xe8, 0x55, 0xcc
}
A.2.3. Role-specific Elements for 4096-bit FFC group
unsigned char group16_initiator[512] = {
0x79, 0x8f, 0xfe, 0xed, 0x53, 0x08, 0x41, 0x73,
0xba, 0x89, 0x66, 0x8d, 0xf0, 0x18, 0xee, 0xe0,
0x76, 0xda, 0x5f, 0xf8, 0x55, 0x36, 0x53, 0x71,
0xd3, 0xfd, 0xf5, 0x30, 0xd9, 0xa0, 0xd2, 0x30,
0x2c, 0x16, 0x38, 0x0a, 0x2b, 0x91, 0x6e, 0x02,
0xc9, 0x27, 0x52, 0xf2, 0x51, 0x0e, 0xe3, 0x1f,
0xbb, 0x2b, 0x8b, 0xad, 0xa8, 0xc3, 0xf4, 0xc0,
0xba, 0x45, 0xf5, 0xf7, 0x4c, 0x91, 0x6f, 0x86,
0x9a, 0xb8, 0xb1, 0xea, 0x7d, 0x89, 0x91, 0x39,
0xd0, 0xb0, 0x95, 0x98, 0xf1, 0xa9, 0x03, 0x8d,
0xc5, 0x7a, 0x75, 0x36, 0x7a, 0xf8, 0x0b, 0xf6,
0xbf, 0x5c, 0x33, 0xde, 0x7f, 0xed, 0xec, 0x1a,
0x1e, 0xbc, 0x54, 0xf1, 0x5f, 0x5c, 0xfa, 0x2f,
Harkins Expires January 29, 2018 [Page 21]
Internet-Draft PKEX July 2017
0x98, 0x85, 0xe0, 0x6f, 0xb8, 0x2b, 0x16, 0xe9,
0x48, 0x6e, 0xe4, 0xb3, 0x3f, 0x20, 0x66, 0x3b,
0x3d, 0xcf, 0x62, 0xc6, 0xed, 0xe5, 0x2e, 0x7a,
0xac, 0x0b, 0x15, 0x6d, 0x15, 0x4e, 0xcb, 0x23,
0xcd, 0x5a, 0xed, 0x51, 0xf4, 0xbe, 0x52, 0x6b,
0x55, 0x30, 0xe3, 0x57, 0x91, 0x1f, 0xf3, 0xbd,
0x07, 0xd9, 0x8b, 0x32, 0x9d, 0xfb, 0x99, 0xbb,
0x17, 0x81, 0x24, 0xd1, 0x82, 0x10, 0xce, 0x34,
0x77, 0x4f, 0xbc, 0x4d, 0xe6, 0x23, 0xdf, 0x2c,
0x24, 0x8d, 0xf5, 0xf5, 0xf9, 0x93, 0x3d, 0x08,
0x55, 0x31, 0xc8, 0xe5, 0xf3, 0x5b, 0x4c, 0xe2,
0x4a, 0xdf, 0x88, 0x83, 0xc7, 0x84, 0x1b, 0xfa,
0x99, 0x72, 0x1b, 0x13, 0x9e, 0xf6, 0x76, 0xca,
0xa9, 0xa2, 0x7f, 0xd8, 0xc0, 0x9a, 0x46, 0x15,
0x0b, 0x20, 0x4e, 0x53, 0x09, 0xe5, 0x16, 0x67,
0xaf, 0xe5, 0x07, 0xe9, 0x57, 0x2f, 0xdc, 0x38,
0xde, 0x33, 0x19, 0x49, 0x08, 0x05, 0x6f, 0xb9,
0xb0, 0xce, 0x97, 0xab, 0xb5, 0xac, 0x88, 0x4e,
0x7a, 0xbe, 0xd0, 0xaa, 0x74, 0x67, 0x73, 0xe3,
0xd5, 0x04, 0x18, 0x41, 0x51, 0xcd, 0xf5, 0x59,
0x85, 0xb6, 0x4b, 0x63, 0x1f, 0x24, 0x27, 0x18,
0x02, 0x1d, 0xb7, 0x95, 0x45, 0xae, 0x60, 0x3a,
0xcc, 0xcb, 0xca, 0x6f, 0xb8, 0x6f, 0x1b, 0x95,
0xba, 0x46, 0x76, 0x8d, 0xc3, 0x61, 0xd0, 0x86,
0xc3, 0x6c, 0x9a, 0xd9, 0x33, 0xde, 0xce, 0x97,
0x28, 0x69, 0xa3, 0xd4, 0xbc, 0x49, 0x6d, 0x10,
0x8d, 0x31, 0x77, 0x53, 0x94, 0xe3, 0xc5, 0xf9,
0xea, 0xcd, 0xb3, 0x5b, 0xbf, 0x51, 0x6f, 0x57,
0x8b, 0x9f, 0x40, 0x8b, 0x47, 0xa8, 0x77, 0xbe,
0x44, 0x3d, 0x8b, 0x54, 0x63, 0xc3, 0xbb, 0xdc,
0xeb, 0x9e, 0xec, 0xf5, 0x7c, 0x31, 0x69, 0x45,
0xf5, 0x48, 0x2c, 0x84, 0x57, 0x53, 0xe1, 0x20,
0x25, 0x2b, 0x70, 0x3a, 0x4e, 0x9f, 0x36, 0xc3,
0x16, 0xf8, 0x4f, 0xa3, 0x21, 0x66, 0x51, 0x49,
0xc6, 0x6d, 0xac, 0xd0, 0x2a, 0x8e, 0xd4, 0x5d,
0x55, 0x11, 0x1a, 0x31, 0x77, 0xdb, 0xa8, 0xf4,
0x7a, 0xb9, 0x32, 0xe8, 0x54, 0xaf, 0xed, 0x55,
0x6e, 0x87, 0xd0, 0x5c, 0x6d, 0xb9, 0x19, 0x0f,
0xbf, 0x16, 0xa6, 0xc7, 0x7c, 0xa2, 0xd3, 0x95,
0x34, 0xad, 0xfc, 0xc2, 0x0a, 0xfc, 0x23, 0x2f,
0xc7, 0xe9, 0x98, 0x92, 0x90, 0x11, 0x1d, 0xd5,
0xf5, 0xbc, 0xd2, 0x8f, 0x09, 0xb0, 0x43, 0x63,
0x65, 0x51, 0x17, 0xfd, 0x11, 0xee, 0xd2, 0x23,
0xff, 0x9f, 0x4e, 0x39, 0xda, 0xfe, 0x89, 0xc1,
0x9d, 0xf3, 0xe0, 0x31, 0xdd, 0x74, 0x36, 0xb2,
0x9f, 0xfa, 0xd2, 0xd0, 0xfc, 0xc4, 0x37, 0x83,
0xf0, 0x13, 0x1f, 0x8d, 0x80, 0x47, 0x53, 0x93,
0x0c, 0x84, 0x1f, 0x69, 0x08, 0x74, 0x33, 0x29,
Harkins Expires January 29, 2018 [Page 22]
Internet-Draft PKEX July 2017
0x59, 0x5f, 0x62, 0x7d, 0xe2, 0x59, 0x1c, 0x56,
0x52, 0x75, 0xc2, 0x83, 0xad, 0xc0, 0xd4, 0x66,
0x71, 0x6a, 0x1a, 0x61, 0x94, 0xa4, 0xa5, 0x73
}
unsigned char group16_responder[512] = {
0x06, 0x85, 0x8b, 0x2e, 0x0c, 0x05, 0xfd, 0x1b,
0x1f, 0x93, 0xd3, 0xc2, 0xe6, 0x70, 0xc8, 0xe1,
0x17, 0x39, 0xe6, 0x38, 0x75, 0xfd, 0xdd, 0xe6,
0x4a, 0xfe, 0x95, 0x5e, 0xd6, 0x80, 0x17, 0x2c,
0x1d, 0xbb, 0x8c, 0xf7, 0x2d, 0x9b, 0x17, 0x93,
0x4d, 0x92, 0xd3, 0x57, 0xa0, 0xcd, 0x44, 0x37,
0x1d, 0xdf, 0xd3, 0x80, 0x25, 0xa0, 0xa8, 0x51,
0x13, 0xb9, 0x63, 0xec, 0xda, 0xa2, 0x8b, 0xdb,
0x2e, 0x09, 0x9c, 0x93, 0x09, 0x02, 0x64, 0xb4,
0xee, 0xa2, 0x3c, 0x75, 0x0e, 0xbb, 0x31, 0x44,
0xff, 0xf0, 0x7e, 0x99, 0x86, 0x17, 0xe5, 0xc4,
0xf9, 0x39, 0xe1, 0xec, 0xed, 0xd5, 0x13, 0xe9,
0x97, 0xda, 0x2b, 0xb5, 0x1e, 0x23, 0x88, 0x1a,
0xb5, 0x10, 0xda, 0x24, 0x05, 0xe7, 0xdf, 0xc3,
0xc2, 0x24, 0xd2, 0xf4, 0x14, 0x6c, 0xfd, 0x2e,
0x62, 0xa8, 0x00, 0x4e, 0xa9, 0x96, 0x3d, 0x48,
0x4f, 0xcf, 0x62, 0xfe, 0x16, 0x06, 0x56, 0x81,
0x1b, 0x58, 0xca, 0x84, 0xd2, 0x86, 0xad, 0xc6,
0x66, 0xb4, 0x6f, 0x49, 0x91, 0x2a, 0xb5, 0x3b,
0x39, 0xec, 0x88, 0xdf, 0x31, 0x24, 0x44, 0x04,
0x30, 0x4e, 0x91, 0xdd, 0x1f, 0xf7, 0x62, 0x0c,
0x8a, 0xf1, 0xcd, 0xf1, 0xcf, 0x56, 0x42, 0x1d,
0x1b, 0xb2, 0x47, 0x7f, 0x4c, 0x82, 0x88, 0xbe,
0x99, 0x31, 0x96, 0x6e, 0x5f, 0xa0, 0x6a, 0xa0,
0x53, 0x63, 0xdb, 0xb9, 0xe0, 0xe4, 0x8f, 0xa9,
0x44, 0x32, 0x2e, 0x05, 0x70, 0x3b, 0x6e, 0xc3,
0x82, 0x36, 0x51, 0x4c, 0xbe, 0x38, 0x61, 0x54,
0x66, 0x5c, 0x88, 0x42, 0x50, 0x84, 0x1a, 0x69,
0xdf, 0xc5, 0x2b, 0x00, 0x3d, 0xdb, 0xe1, 0x92,
0x69, 0xb4, 0xda, 0xfa, 0x87, 0x43, 0x9e, 0xdd,
0x03, 0x29, 0xd4, 0x06, 0xef, 0x63, 0x60, 0xe3,
0x83, 0xe3, 0x28, 0xd7, 0xa3, 0x47, 0xeb, 0xb7,
0x0a, 0x20, 0x5a, 0x9e, 0x61, 0x68, 0xcc, 0x0b,
0x39, 0xdc, 0x7b, 0x8c, 0x22, 0x0f, 0xc8, 0xd4,
0x0c, 0x44, 0x9c, 0xa2, 0xb4, 0xd2, 0xf4, 0x71,
0xeb, 0xc6, 0x75, 0xb8, 0x53, 0x8c, 0x93, 0x9a,
0xf2, 0xd7, 0xba, 0x45, 0x40, 0xef, 0x56, 0xaf,
0xdd, 0x1b, 0xcc, 0x0e, 0xe0, 0x3b, 0x2f, 0xd5,
0xc5, 0xc7, 0x36, 0x37, 0xc0, 0x5e, 0xff, 0xb1,
0x31, 0xce, 0xce, 0xc3, 0x28, 0xb7, 0x84, 0x88,
0xe2, 0x7f, 0x11, 0x62, 0xb1, 0x14, 0x41, 0xe2,
0x7e, 0xfb, 0x31, 0x0e, 0x5b, 0xba, 0x27, 0xf7,
Harkins Expires January 29, 2018 [Page 23]
Internet-Draft PKEX July 2017
0xa0, 0xce, 0xa0, 0xb8, 0xdd, 0xbe, 0xc4, 0x74,
0xe0, 0xc9, 0x50, 0x71, 0x16, 0x81, 0x42, 0x2a,
0xa9, 0xda, 0x2e, 0x3a, 0x85, 0x0b, 0x62, 0x5a,
0x55, 0x31, 0x31, 0xc4, 0xda, 0x4b, 0x36, 0x9a,
0xa6, 0x0b, 0x78, 0x51, 0x50, 0xea, 0x44, 0x07,
0x6d, 0xf7, 0x49, 0xb0, 0xea, 0x7e, 0x12, 0x92,
0x88, 0x5e, 0xb8, 0xee, 0x0b, 0xa9, 0xd8, 0x04,
0xbe, 0xd8, 0x5d, 0x8e, 0x0a, 0xea, 0x5c, 0xce,
0xf5, 0x2d, 0x80, 0xff, 0x57, 0x07, 0x0c, 0x06,
0x20, 0xaf, 0xb5, 0x32, 0x16, 0xb5, 0x79, 0x60,
0xce, 0x3b, 0xb8, 0x55, 0x4c, 0xf5, 0x58, 0x90,
0xeb, 0xae, 0x48, 0x04, 0x8b, 0x76, 0xfc, 0x66,
0x18, 0x70, 0x13, 0x5c, 0x85, 0xa4, 0x18, 0xf1,
0xbb, 0x06, 0x4e, 0x59, 0x19, 0x75, 0x4d, 0xaf,
0x97, 0x6b, 0x1c, 0x82, 0x2f, 0xbf, 0x91, 0xbb,
0xb7, 0x93, 0x21, 0xf2, 0xca, 0xf7, 0xec, 0x31,
0xf2, 0x05, 0x73, 0x1e, 0x69, 0x30, 0xd1, 0xd9,
0xef, 0x4f, 0x57, 0xc5, 0xf2, 0x46, 0xbf, 0xe8,
0x81, 0xb6, 0x24, 0xdb, 0xf3, 0x67, 0x27, 0x97,
0xb8, 0x04, 0x8c, 0xa3, 0xfe, 0xda, 0x6b, 0x9d,
0x51, 0xba, 0xbd, 0xb5, 0xca, 0xfe, 0x73, 0xce,
0x48, 0x9d, 0x28, 0x30, 0x7d, 0x53, 0x63, 0xc7
}
A.2.4. Role-specific Elements for 8192-bit FFC group
unsigned char group18_initiator[1024] = {
0x5b, 0x92, 0xc0, 0x76, 0x71, 0x48, 0x5e, 0x4d,
0x9d, 0xdf, 0xde, 0xc3, 0xcc, 0x32, 0x6e, 0xf1,
0x90, 0xef, 0x71, 0x86, 0xde, 0x55, 0x60, 0x3e,
0x24, 0x3e, 0xc2, 0x38, 0x09, 0x65, 0x56, 0xfb,
0x2b, 0x8b, 0x97, 0x07, 0x19, 0xac, 0xaf, 0x59,
0x32, 0xd7, 0x65, 0x19, 0xa2, 0x02, 0x83, 0xa3,
0x72, 0xc2, 0x2c, 0xe8, 0x15, 0x58, 0x0d, 0xb8,
0x1a, 0xad, 0xe3, 0xbc, 0xc0, 0x82, 0xab, 0x42,
0x9a, 0x7e, 0x0d, 0x39, 0x6a, 0x81, 0x3e, 0x72,
0xee, 0xba, 0x58, 0x01, 0xe6, 0x36, 0x9f, 0x82,
0x49, 0xa3, 0x6a, 0x88, 0x59, 0x0f, 0x77, 0x6b,
0x4d, 0x6a, 0x36, 0x25, 0xf0, 0xbc, 0x75, 0x53,
0x45, 0x1b, 0x02, 0x4c, 0x99, 0x5d, 0x51, 0x87,
0x41, 0x3c, 0xcc, 0x54, 0x6a, 0xdc, 0x6e, 0x22,
0xb5, 0x7d, 0xa9, 0x65, 0x90, 0xd3, 0x38, 0x4c,
0xa8, 0x26, 0x22, 0x57, 0xd8, 0x55, 0xc0, 0xc9,
0x9a, 0x62, 0x08, 0x71, 0x2b, 0x55, 0xde, 0x89,
0xd4, 0xf8, 0xab, 0x5f, 0x55, 0x42, 0xc0, 0x40,
0x60, 0x61, 0x1b, 0x68, 0x01, 0x80, 0x67, 0x27,
0x95, 0x8e, 0x6b, 0xcd, 0xc1, 0x04, 0x35, 0x96,
0x8e, 0x15, 0x1e, 0xd3, 0x01, 0x7d, 0x81, 0x38,
Harkins Expires January 29, 2018 [Page 24]
Internet-Draft PKEX July 2017
0xe8, 0xbf, 0xd1, 0xa8, 0x31, 0xd5, 0x49, 0x11,
0x0d, 0x78, 0x2f, 0x61, 0x31, 0xfc, 0xcc, 0x11,
0x4f, 0x09, 0xa1, 0x13, 0x2b, 0x0e, 0x73, 0xbc,
0x1f, 0xef, 0x01, 0x7d, 0xd3, 0x26, 0xe3, 0xda,
0xa9, 0xaa, 0x15, 0xaf, 0x47, 0xe5, 0xc0, 0x39,
0x29, 0xa3, 0x68, 0xfc, 0x03, 0xaa, 0x20, 0xc0,
0xf8, 0xc5, 0xe2, 0xe3, 0x03, 0x0d, 0x3c, 0x20,
0x7c, 0xbf, 0xa5, 0x1b, 0xd9, 0x92, 0x2d, 0x79,
0x42, 0x42, 0xe8, 0x92, 0x25, 0x9a, 0x94, 0x54,
0x40, 0xec, 0x8d, 0x55, 0x26, 0x71, 0xb3, 0x58,
0x2c, 0x0b, 0x81, 0x4d, 0x53, 0xb8, 0x52, 0xf9,
0x1b, 0xb1, 0x75, 0x60, 0xd4, 0x4b, 0x45, 0x72,
0xa6, 0x61, 0x20, 0x96, 0xaa, 0x3b, 0xb9, 0x50,
0x81, 0xe3, 0x93, 0xde, 0x4b, 0x80, 0xa2, 0xbd,
0x20, 0x64, 0x63, 0xe2, 0x48, 0xc8, 0xec, 0x82,
0x07, 0xa1, 0x7b, 0x45, 0x2a, 0xfb, 0xe9, 0x2f,
0xa1, 0xf0, 0x69, 0x36, 0x2d, 0x4f, 0x1a, 0x85,
0xf3, 0x58, 0x34, 0xe6, 0x0a, 0x9e, 0xe9, 0x9a,
0x77, 0xe5, 0xf9, 0xa4, 0xc4, 0x14, 0xa2, 0x43,
0xdd, 0xaa, 0x03, 0x17, 0x71, 0x55, 0x62, 0xf4,
0xf5, 0x9c, 0x5f, 0x2f, 0xe7, 0x6f, 0xde, 0xa4,
0x7a, 0xbb, 0x9d, 0xb5, 0x8d, 0xc3, 0x95, 0xf9,
0x54, 0x06, 0xba, 0xd1, 0x31, 0xcf, 0x03, 0x6c,
0x7a, 0x53, 0xd5, 0x76, 0x97, 0x4c, 0xbd, 0x23,
0x59, 0xff, 0xfe, 0xea, 0xd3, 0xd1, 0x86, 0x10,
0x2c, 0xf9, 0x9f, 0xc8, 0xd3, 0x45, 0x44, 0x2f,
0x5a, 0xcf, 0x86, 0x8e, 0x1c, 0xc2, 0xb7, 0x04,
0x75, 0x74, 0x78, 0xdf, 0x7a, 0x6f, 0xaf, 0x56,
0x03, 0x93, 0x19, 0x4f, 0x4d, 0x73, 0x11, 0xc9,
0x34, 0x90, 0x1a, 0x76, 0x18, 0x76, 0xa7, 0x19,
0xe4, 0x5e, 0x66, 0x10, 0x2e, 0x0a, 0xbe, 0x7c,
0x64, 0xd2, 0xd3, 0xbb, 0x18, 0x58, 0x86, 0xd9,
0x54, 0x58, 0xf5, 0xeb, 0x86, 0xac, 0x61, 0x48,
0xbc, 0x95, 0x1e, 0x13, 0xab, 0xef, 0x6e, 0xdf,
0xbc, 0xa5, 0x78, 0x10, 0x87, 0x43, 0x9a, 0xd6,
0xd6, 0x10, 0x30, 0xc0, 0xf5, 0x9b, 0x09, 0xc4,
0x2c, 0xed, 0x8b, 0xeb, 0xc7, 0x3c, 0x12, 0xc5,
0x1c, 0xf1, 0x88, 0xfd, 0x15, 0x45, 0xdb, 0xb3,
0x35, 0x87, 0x40, 0xf8, 0x8a, 0xd1, 0x07, 0x32,
0x2b, 0xf7, 0x4a, 0x77, 0xb5, 0x69, 0x4a, 0x20,
0xdd, 0x69, 0x1e, 0x38, 0xac, 0x0b, 0x31, 0xda,
0x43, 0x5d, 0xf0, 0x94, 0x22, 0x8d, 0x4a, 0x26,
0xda, 0x91, 0xdf, 0xb7, 0xdd, 0xfb, 0x97, 0x88,
0x7a, 0x43, 0x5e, 0xf3, 0x36, 0xbd, 0xef, 0xc0,
0xe6, 0x7f, 0xd1, 0x81, 0x5b, 0xd6, 0x1b, 0x01,
0x89, 0x19, 0x1d, 0x0e, 0xd0, 0x1a, 0x3a, 0x56,
0x82, 0xf6, 0x2c, 0xdf, 0x6a, 0x42, 0xf5, 0x44,
0x57, 0x61, 0x95, 0xdc, 0x9d, 0x4c, 0x15, 0xc0,
Harkins Expires January 29, 2018 [Page 25]
Internet-Draft PKEX July 2017
0x29, 0x42, 0x55, 0x77, 0x28, 0xc8, 0x7c, 0xe2,
0xc8, 0x44, 0xbd, 0xdd, 0x8e, 0xe1, 0xb8, 0xa3,
0xa6, 0xb1, 0xa5, 0xfc, 0x9f, 0xed, 0x5f, 0xd7,
0x58, 0xee, 0xe9, 0xa8, 0x1e, 0x11, 0x1a, 0x8c,
0xf6, 0xea, 0x45, 0x8f, 0x41, 0x4d, 0xb9, 0x7f,
0xe9, 0xd2, 0x90, 0x8c, 0xed, 0x0a, 0xd1, 0x12,
0x48, 0x9b, 0x5e, 0x8a, 0x98, 0xc8, 0x0e, 0x71,
0xff, 0x35, 0xa3, 0xc0, 0x17, 0x1c, 0x29, 0xe7,
0x30, 0x47, 0x5f, 0x22, 0x62, 0x1b, 0xde, 0xb9,
0xeb, 0x20, 0xcc, 0xeb, 0xfc, 0x7d, 0x38, 0x1e,
0xce, 0x8a, 0x4e, 0xa8, 0xfe, 0xba, 0xa9, 0xfc,
0x44, 0x8a, 0xcf, 0x0a, 0xe3, 0xf1, 0x91, 0x63,
0xaf, 0xf2, 0x7d, 0x52, 0x2a, 0x6d, 0x38, 0xcf,
0x10, 0xd5, 0xa3, 0xa1, 0xb0, 0xcc, 0x74, 0x08,
0xe9, 0x97, 0xe1, 0x7e, 0xd8, 0xd1, 0x3f, 0x4e,
0x8d, 0x6d, 0x4e, 0x3e, 0x33, 0xc7, 0xae, 0x28,
0xb6, 0x6a, 0xd0, 0x15, 0xf3, 0xd6, 0xfd, 0x11,
0x3e, 0xbc, 0x65, 0xe6, 0xf7, 0xb4, 0xfe, 0x55,
0x03, 0x4d, 0x1f, 0x4f, 0x8b, 0xef, 0x8d, 0x11,
0xa2, 0x9b, 0x42, 0x58, 0xf4, 0xdf, 0x0c, 0xf2,
0x80, 0x0e, 0x02, 0xff, 0xe8, 0x46, 0x0d, 0xae,
0x50, 0x41, 0x14, 0x37, 0x5d, 0x82, 0x26, 0x96,
0x9f, 0x1d, 0xff, 0x9e, 0xe0, 0x01, 0x24, 0x19,
0xe8, 0xca, 0xe7, 0x7b, 0xaa, 0xef, 0x05, 0x4a,
0x8a, 0xdd, 0x3b, 0xe8, 0x93, 0xf0, 0x21, 0xab,
0x7f, 0x77, 0xcd, 0xc1, 0x71, 0x9f, 0x6b, 0x2b,
0x64, 0xfb, 0x43, 0x9e, 0x92, 0x33, 0x68, 0xe6,
0x51, 0xc1, 0x16, 0x3d, 0xde, 0xf8, 0x85, 0x8a,
0xb6, 0x6c, 0x96, 0x7a, 0x6b, 0x12, 0xd8, 0x18,
0x30, 0x5e, 0x0c, 0x82, 0xff, 0xff, 0xd0, 0xf7,
0x9c, 0x23, 0x30, 0x61, 0x80, 0x5b, 0xde, 0xd9,
0x35, 0x16, 0xdd, 0x6a, 0x5b, 0xbe, 0x5a, 0x1d,
0x77, 0x37, 0x2b, 0xee, 0x00, 0x61, 0xef, 0xfe,
0xa8, 0x3f, 0x2e, 0xd6, 0x8e, 0x3a, 0x0f, 0x03,
0xae, 0x46, 0x01, 0x0c, 0x75, 0x8c, 0x42, 0x9b,
0x24, 0x02, 0x4b, 0xdb, 0xb8, 0x98, 0x31, 0xc7,
0xd0, 0xd9, 0xb1, 0x89, 0x4a, 0x54, 0x74, 0xc0,
0x68, 0x5d, 0xe7, 0x62, 0xe4, 0x44, 0x44, 0x5e,
0x17, 0x75, 0x34, 0x96, 0xbe, 0xf1, 0x94, 0x49,
0x14, 0xe7, 0x17, 0x79, 0xf6, 0xab, 0xe8, 0xf4,
0x47, 0x77, 0x74, 0x10, 0x51, 0x3b, 0x30, 0x8e,
0x8e, 0x00, 0x4f, 0x0e, 0x75, 0x03, 0xc7, 0x48,
0xfb, 0xf8, 0x50, 0xc7, 0xe5, 0xfc, 0xe2, 0x7d,
0x07, 0x90, 0xd5, 0x91, 0x6a, 0xce, 0x14, 0x12,
0xab, 0xe6, 0x65, 0x64, 0xfb, 0x03, 0xce, 0xdf,
0xf1, 0x0b, 0x11, 0x82, 0x5a, 0x11, 0xf6, 0xf9,
0xd6, 0xf2, 0xfe, 0xd4, 0x72, 0x60, 0x80, 0xd4,
0x53, 0x86, 0xe6, 0xfc, 0xb7, 0xc0, 0x03, 0x4d,
Harkins Expires January 29, 2018 [Page 26]
Internet-Draft PKEX July 2017
0x3c, 0x32, 0xe9, 0xfd, 0x46, 0x9e, 0x81, 0x6a,
0x72, 0xd6, 0x9c, 0x14, 0x70, 0x47, 0xbe, 0x35,
0xef, 0xb2, 0xbb, 0x0a, 0xca, 0x84, 0xc9, 0x15,
0xac, 0x83, 0x6b, 0x83, 0xe8, 0x36, 0x5d, 0x27,
0xc0, 0x25, 0xc8, 0x92, 0x69, 0x6b, 0x51, 0x6a,
0xc2, 0x8f, 0x9c, 0x8b, 0xf5, 0x35, 0x1e, 0x31,
0x4b, 0xf7, 0xd6, 0x40, 0xa7, 0x1c, 0xe4, 0xa2,
0x00, 0x3c, 0x78, 0x78, 0x8f, 0x27, 0x24, 0x7e,
0x0b, 0x7f, 0xf6, 0xb0, 0x66, 0xf4, 0x79, 0x46,
0x2e, 0x5b, 0x11, 0xca, 0x9b, 0x93, 0x4e, 0x99,
0x2c, 0xd2, 0x2d, 0x88, 0x84, 0xf1, 0x1e, 0x0e
}
unsigned char group18_responder[1024] = {
0xdf, 0x63, 0xdc, 0x3a, 0x74, 0xbd, 0x83, 0x8e,
0x72, 0x90, 0x81, 0xf0, 0x85, 0x65, 0x86, 0x07,
0x06, 0x05, 0xed, 0x93, 0x73, 0xa5, 0xbb, 0x88,
0x42, 0x17, 0x8a, 0x10, 0x33, 0xc3, 0x6e, 0x9b,
0x3b, 0x68, 0x33, 0x30, 0xa2, 0x3f, 0xb2, 0xa3,
0x2d, 0x6b, 0xec, 0x34, 0x5a, 0xe7, 0x6a, 0xc1,
0x11, 0xc8, 0xa5, 0x3d, 0x6c, 0xc5, 0xf7, 0x48,
0xca, 0xac, 0xa6, 0x10, 0x0b, 0x7c, 0x93, 0xe9,
0x45, 0x4d, 0xa7, 0x00, 0x30, 0xd2, 0xf5, 0xaf,
0x93, 0xf1, 0xa5, 0x8a, 0x9f, 0x10, 0x14, 0xe6,
0x6a, 0xe0, 0x5a, 0xe6, 0xea, 0x8b, 0x21, 0xbb,
0x6a, 0x1f, 0x6c, 0x8c, 0x0b, 0x01, 0xda, 0xfd,
0x4f, 0x0b, 0x7f, 0xe9, 0x46, 0x27, 0x8e, 0xaa,
0x64, 0xd1, 0xd5, 0x40, 0xc9, 0xf7, 0x47, 0xef,
0x9f, 0x7c, 0xce, 0x6c, 0x41, 0xd2, 0x9c, 0x47,
0x09, 0x6e, 0xc7, 0xc2, 0xdc, 0x7d, 0x7e, 0xce,
0x04, 0x6f, 0xf9, 0xc1, 0x86, 0x56, 0x1b, 0x88,
0x7f, 0x62, 0x33, 0x3b, 0xca, 0xb9, 0xd4, 0x7d,
0x24, 0xfa, 0x9f, 0xd8, 0xf8, 0x63, 0x91, 0x72,
0x45, 0x82, 0x4d, 0x9f, 0xd7, 0x9d, 0xc8, 0x0b,
0x4c, 0x6a, 0xc5, 0xf4, 0xec, 0x77, 0x3e, 0xfd,
0xb7, 0x6b, 0xe0, 0x86, 0x32, 0x41, 0x25, 0xfe,
0x43, 0x03, 0x0a, 0x07, 0x90, 0x75, 0xd5, 0xca,
0x48, 0x23, 0xfb, 0x80, 0x5f, 0x22, 0xfe, 0x1c,
0xba, 0x48, 0x2c, 0x28, 0x78, 0x5c, 0xc4, 0x98,
0xad, 0xb7, 0xa6, 0x78, 0x5f, 0x84, 0x3a, 0xb6,
0x96, 0xd5, 0xad, 0x88, 0x60, 0xb9, 0x09, 0x00,
0xbb, 0x7d, 0x5c, 0xd6, 0x17, 0xfe, 0x18, 0x8e,
0x07, 0x10, 0xc3, 0xe9, 0xd0, 0xb8, 0xe2, 0xfa,
0x00, 0xae, 0xa1, 0xcd, 0x86, 0x33, 0xda, 0x4b,
0x0c, 0x34, 0xa1, 0x6e, 0x19, 0x0b, 0xdb, 0xef,
0xb0, 0xf6, 0x86, 0xc6, 0xe3, 0x8c, 0x9c, 0x53,
0x15, 0x16, 0x04, 0xd9, 0xa8, 0xa7, 0x38, 0xc1,
0x43, 0x9d, 0x7e, 0x33, 0x16, 0x1a, 0x8d, 0x33,
Harkins Expires January 29, 2018 [Page 27]
Internet-Draft PKEX July 2017
0xe8, 0x2b, 0x47, 0xaf, 0x4c, 0xd0, 0x96, 0x87,
0x5b, 0x57, 0x27, 0xc3, 0x1a, 0xf7, 0x12, 0xfd,
0x8a, 0x64, 0xa0, 0xc9, 0x51, 0xc9, 0x95, 0xcb,
0x7b, 0x9d, 0x97, 0xda, 0x3c, 0xae, 0x87, 0x1c,
0x08, 0xa8, 0xb2, 0x3b, 0x92, 0xb7, 0x52, 0x97,
0x99, 0x9c, 0x52, 0x92, 0xcc, 0xba, 0xbe, 0x16,
0xf7, 0xac, 0x08, 0xb5, 0x1a, 0x99, 0x99, 0xee,
0x33, 0x3a, 0x2a, 0xea, 0x70, 0xbe, 0xcc, 0xfd,
0xc7, 0x6b, 0xf3, 0xa9, 0x9d, 0x66, 0x87, 0x1b,
0x26, 0x0e, 0xf5, 0x04, 0x33, 0x82, 0x25, 0x75,
0x74, 0x37, 0xbd, 0xfe, 0x78, 0xa2, 0x4a, 0x77,
0xda, 0xef, 0x84, 0xfd, 0x5c, 0x1d, 0x09, 0xc7,
0xd8, 0xc2, 0x97, 0xf8, 0xd0, 0x96, 0x6f, 0xf0,
0x54, 0xea, 0x5e, 0x14, 0xb6, 0x9c, 0x16, 0x96,
0xcd, 0x56, 0x3e, 0x49, 0xef, 0x8f, 0xbf, 0xc1,
0x59, 0xd6, 0x0c, 0xa0, 0xd6, 0x6b, 0xff, 0x34,
0xe5, 0x68, 0x70, 0x6b, 0x00, 0x87, 0xac, 0x4e,
0x7e, 0x44, 0xa2, 0x04, 0xa2, 0x96, 0xfc, 0x73,
0xe7, 0xe2, 0x7f, 0xc6, 0x0b, 0x17, 0xdb, 0xa6,
0x45, 0xa8, 0x72, 0x61, 0x08, 0xc8, 0x4c, 0x19,
0x2d, 0x27, 0x0b, 0x4f, 0xb9, 0xc0, 0x55, 0xd6,
0x6d, 0x11, 0xd7, 0x15, 0x0d, 0xef, 0x97, 0x08,
0xd3, 0x22, 0xd8, 0x03, 0x7f, 0x91, 0xe0, 0x0e,
0xe4, 0x70, 0x75, 0x47, 0x33, 0xd9, 0x80, 0x08,
0x5f, 0xc9, 0xea, 0x91, 0xd4, 0x4e, 0x80, 0x08,
0xb3, 0x83, 0x37, 0xba, 0xd2, 0xe0, 0x6d, 0x44,
0x83, 0x9a, 0xf1, 0xa6, 0x83, 0xc4, 0x5a, 0xd2,
0x3f, 0x50, 0x7a, 0x19, 0xed, 0x82, 0xda, 0x02,
0x6f, 0xbe, 0x27, 0x91, 0xd6, 0x7e, 0x11, 0xc1,
0x95, 0x3a, 0x6a, 0x61, 0x80, 0x6c, 0x23, 0x1f,
0xcd, 0x8d, 0xac, 0x5c, 0x4c, 0x14, 0xee, 0xde,
0x08, 0x15, 0x87, 0xae, 0x2d, 0xf4, 0x77, 0x81,
0xcb, 0x39, 0x9a, 0x51, 0xb1, 0x3e, 0xc6, 0xd5,
0xcd, 0xa2, 0x3a, 0x15, 0x6a, 0x73, 0x2e, 0x78,
0x24, 0x16, 0xb8, 0xd2, 0x3e, 0xb4, 0x0c, 0xc2,
0x0e, 0x67, 0xea, 0xe9, 0x9c, 0xce, 0x5c, 0x6a,
0x29, 0x27, 0xe1, 0x3f, 0xac, 0x9d, 0x31, 0xb8,
0xda, 0x2f, 0x94, 0x6e, 0xfc, 0x33, 0xab, 0x54,
0xf9, 0x8e, 0xe8, 0xbf, 0x8e, 0x33, 0x62, 0xab,
0x1f, 0xca, 0x17, 0x68, 0x89, 0x27, 0x19, 0x52,
0xb1, 0x4c, 0xd1, 0x04, 0xb8, 0x8d, 0xfe, 0xc2,
0xa4, 0xbf, 0xb8, 0x4e, 0x7c, 0x24, 0x2f, 0xaa,
0x8c, 0x57, 0x3c, 0x60, 0xe8, 0xd5, 0x1e, 0x7f,
0x8b, 0x85, 0x0e, 0xfb, 0x0e, 0xbd, 0xed, 0x75,
0x3f, 0x35, 0xeb, 0xb7, 0x35, 0x60, 0x53, 0x8f,
0x7d, 0x86, 0xbc, 0x98, 0x8b, 0x2e, 0x22, 0x33,
0x5e, 0x60, 0x49, 0x6d, 0xc3, 0xe0, 0xaa, 0xec,
0x5e, 0x67, 0x87, 0xd8, 0x20, 0x92, 0x71, 0x34,
Harkins Expires January 29, 2018 [Page 28]
Internet-Draft PKEX July 2017
0x46, 0xa4, 0xf4, 0x2d, 0x02, 0xaf, 0x64, 0x45,
0xef, 0xea, 0xb3, 0x84, 0x39, 0xd6, 0x6b, 0xaf,
0x7d, 0x63, 0xd3, 0x50, 0xf9, 0x95, 0xaf, 0xf7,
0xf3, 0x8a, 0x6f, 0x59, 0xf1, 0x32, 0x37, 0x3d,
0x6c, 0xd4, 0xaa, 0x17, 0xd7, 0x13, 0x19, 0xa7,
0x51, 0x98, 0x21, 0x89, 0x26, 0x12, 0xe1, 0xed,
0x78, 0x04, 0x33, 0xd7, 0xc6, 0xf4, 0xe2, 0x39,
0x5c, 0x37, 0xdb, 0x16, 0x42, 0xf9, 0x0a, 0x3d,
0xee, 0x4b, 0x96, 0xbd, 0x60, 0x1f, 0x36, 0xbb,
0xe6, 0x15, 0x95, 0x47, 0x7f, 0x8f, 0x2e, 0xff,
0x59, 0x9b, 0xfc, 0x99, 0x13, 0x87, 0xac, 0x85,
0xd9, 0x84, 0x0c, 0x99, 0x95, 0xe8, 0x2b, 0xdf,
0xae, 0x64, 0x7e, 0x24, 0x85, 0x67, 0x9c, 0x86,
0x51, 0x8a, 0x61, 0x6c, 0x17, 0x24, 0x89, 0xba,
0x2f, 0xfa, 0x9d, 0x3d, 0xa6, 0x51, 0xce, 0x85,
0xf8, 0x95, 0x78, 0xeb, 0x00, 0x51, 0x06, 0xb4,
0x8b, 0x02, 0x1b, 0x1c, 0xf7, 0x13, 0xcb, 0xee,
0x83, 0x98, 0xdc, 0xab, 0xed, 0x57, 0x62, 0x78,
0x1c, 0xc5, 0x5c, 0xac, 0xa6, 0x23, 0x68, 0xd0,
0xa5, 0xda, 0x43, 0x2d, 0x61, 0x73, 0x66, 0x03,
0xea, 0xc9, 0xad, 0x7e, 0xe3, 0x54, 0xa9, 0x53,
0x3e, 0x23, 0x4c, 0x6a, 0x15, 0x70, 0xa5, 0x2c,
0xee, 0xcd, 0x4d, 0x7e, 0x41, 0x6f, 0xa6, 0xc5,
0x1c, 0x24, 0x37, 0x58, 0x00, 0x81, 0xd9, 0xb2,
0xf7, 0x9a, 0x9c, 0xa3, 0xf5, 0xc6, 0x31, 0xc1,
0xb2, 0x8b, 0x3d, 0xec, 0xbe, 0x21, 0xe7, 0x53,
0x0f, 0xb8, 0x87, 0x76, 0xb5, 0x76, 0xcc, 0x50,
0x03, 0x51, 0x8a, 0xa5, 0xb9, 0x50, 0xc7, 0x38,
0xaf, 0x98, 0x01, 0xdf, 0x77, 0xb2, 0x9f, 0xe8,
0xa5, 0x5b, 0x9d, 0x48, 0x3a, 0x82, 0xe1, 0x10,
0xc8, 0x34, 0xc1, 0x07, 0x8f, 0x63, 0x60, 0x3e,
0x25, 0xb6, 0x33, 0xbc, 0x15, 0xce, 0x99, 0x39,
0x62, 0x83, 0x5b, 0xbc, 0x22, 0xb9, 0x0b, 0xd3,
0x97, 0x2b, 0x87, 0xee, 0x85, 0xd6, 0x72, 0x01,
0xb8, 0xdb, 0xe1, 0xdd, 0x5f, 0x61, 0x5f, 0x81,
0x44, 0xcc, 0x65, 0x71, 0x44, 0xb7, 0xca, 0x48,
0xd2, 0x33, 0x7b, 0x56, 0xe6, 0x07, 0xb8, 0xc5,
0x6c, 0xb0, 0xf6, 0x72, 0x69, 0x75, 0xf7, 0xfc,
0xd5, 0xab, 0xe0, 0xbb, 0x65, 0xcb, 0xd8, 0x4a,
0xae, 0x99, 0x58, 0x5c, 0xe3, 0x61, 0x38, 0x07,
0x97, 0xee, 0xa7, 0x67, 0x48, 0xb7, 0x9e, 0xc0,
0xe9, 0xf5, 0x3c, 0x18, 0x3d, 0xb2, 0x06, 0x0f,
0x75, 0x8d, 0xb8, 0x82, 0xfa, 0x6d, 0x30, 0x91,
0x8b, 0x3b, 0xee, 0xf8, 0x27, 0x40, 0xec, 0x26,
0x08, 0xd4, 0xca, 0x00, 0x8f, 0x28, 0xa2, 0x38,
0xd9, 0xa0, 0x42, 0xc4, 0x51, 0x8b, 0x6c, 0xce
}
Harkins Expires January 29, 2018 [Page 29]
Internet-Draft PKEX July 2017
Author's Address
Dan Harkins
HP Enterprise
1322 Crossman avenue
Sunnyvale, California 94089
USA
Phone: +1 415 997 9834
Email: dharkins@lounge.org
Harkins Expires January 29, 2018 [Page 30]